PML: Toward a High-Level Formal Language for Biological Systems Bor-Yuh Evan Chang and Manu Sridharan Computer Science Division University of California, Berkeley BioConcur, Marseille September 6, 2003

2 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Why Formal Models for Biology? Experiments have led to an enormous wealth of (detailed) knowledge but in a fragmented form –serve as a common language for sharing modular, compositional, varying levels of abstraction Much information described through prose or graph-like diagrams with loose semantics –make assumptions explicit Mathematical abstraction convenient for reasoning and simulation

3 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Previous Abstractions Chemical kinetic models –can derive differential equations –well-studied, with considerable theoretical basis –variables do not directly correspond with biological entities –may become difficult to see how multiple equations relate to each other

4 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Previous Abstractions Pathway Databases (e.g., EcoCyc, KEGG) –store information in a symbolic form and provide ways to query the database –behavior of biological entities not directly described Petri nets –place = particular state of a molecular specie, token = molecule, transition = reaction

5 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Previous Abstractions Concurrent computational processes –each biological entity is a process that may carry some state and interacts with other processes –each biological entity described by a “program” –prior proposals based on process algebras, such as the  -calculus [Regev et al. ’01] –we take this view

6 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Modeling in the  -calculus The  -calculus is concise and compact, yet powerful [Milner ’90] –take this as the underlying machine model –not looking for another machine model However, it is far too low-level for direct modeling (ad-hoc structuring)

7 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Informal Graphical Diagrams Protein Enzyme ProteinEnzyme Protein k k -1 k cat sites domains rules

8 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems PML: Enzyme Enzyme bind_substrate parameterized declared in outer scope interactions within the complex

9 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems PML: Protein Protein bind_substratebind_product

10 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems PML: A Simple System

11 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Compartments Critical part of biological pathways –prevents interactions that would otherwise occur Description of the behavior of a molecule should not depend on the compartment Regev et al. use “private” channels in the  - calculus for both complexing and compartmentalization

12 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems PML: Simple Compartments Example MolA MolB bind_a

13 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems PML: Simple Compartments Example MolA MolB ERCytosol CytERBridge

14 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems PML: Simple Compartments Example MolB ERCytosol CytERBridge MolA

15 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems PML: Summary Domains –set of mutually dependent binding sites –defines at the lowest-level the reactions a biological entity can undergo Groups –static structure for controlling namespace –may represent a large biological entity large complex, a system, etc. Compartments –special groups that define boundaries

16 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Semantics of PML Defined in terms of the  -calculus via two translations –from PML to CorePML “flattens” compartments, removes bridges

17 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Semantics of PML –from CorePML to the  -calculus

18 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Larger Models Modeled a general description of ER cotranslational-translocation –unclearly or incompletely specified aspects became apparent e.g., can the signal sequence and translocon bind without SRP? Yes [Herskovits and Bibi ’00] Extended to model targeting ER membrane with minor modifications

19 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Benefits of PML Easier to write and understand because of a more direct biological metaphor Block structure for controlling namespace and modularity Special syntax for compartments –separate complexing from compartmentalization

20 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Future Work Naming? Proximity of molecules Integrating quantitative information (reaction rates, etc.) –start from work by Priami et al. Compartment fusion and fission Type checking PML specifications Exceptional / higher-level specifications Graphical and simulation tools

Syntax of PML

23 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Syntax of PML

24 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Syntax of PML

The  -calculus

26 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems The  -calculus Syntax Operational Semantics

27 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems The  -calculus Congruence

Example: Cotranslational Translocation

29 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Example: Cotranslational Translocation Ribosome translates mRNA exposing a signal sequence Signal sequence attracts SRP stopping translation SRP receptor (on ER membrane) attracts SRP Signal sequence interacts with translocon, SRP disassociates resuming translation Signal peptidase cleaves the signal sequence in the ER lumen, Hsc70 chaperones aid in protein folding

30 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Example: Cotranslational Translocation

31 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Example: Cotranslational Translocation

32 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Example: Cotranslational Translocation

33 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Example: Cotranslational Translocation

34 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Example: Cotranslational Translocation

35 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Example: Cotranslational Translocation

36 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Example: Cotranslational Translocation

37 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Computer Systems vs. Biological Processes Similarities –elementary pieces build-up components that in turn build-up large components and so forth to create highly complex systems –all systems seem to have similar cores but exhibit great diversity Differences! –theory of computation and computer systems are purely man-made (controlled-design) but biology is observational

38 9/6/2003 PML: Toward a High-Level Formal Language for Biological Systems Model of Concurrent Computation Must choose a machine model as a basis –The  -calculus [Milner ’90 and others] A formalism aimed at capturing the essence of concurrent computation. –focuses on communication by message passing System composed of processes Communication on channels –send: send message m on channel c –receive: receive message on channel c, call it x –Many variants—the stochastic  -calculus